[tex](\frac{3}{2},\frac{3\sqrt{3}}{2})[/tex]
Explanation
a coordiante given in polar form is has the structure
[tex]\begin{gathered} \langle r,\theta\rangle \\ whe\text{re r is the magnitude of the vector} \\ \theta\text{ is the angle with the positive x-axis} \end{gathered}[/tex]
now, to convert from polar to Cartesian coordiantes we need to apply the formula
[tex]\begin{gathered} x-coordinate\text{= r*cos }\theta \\ y-coordinater\text{= r}*\sin\theta \end{gathered}[/tex]
Step 1
[tex](-3,-\frac{2\pi}{3})[/tex]
so,
a)b)let
[tex]\begin{gathered} r=-3 \\ \theta=\frac{-2\pi}{3} \end{gathered}[/tex]
b)Now,replace
[tex]\begin{gathered} x-coordiante=r*cos\text{ }\theta \\ x-coordiante=-3*cos(\frac{-2\pi}{3})= \\ x-coordiante=-3*-0.5=1.5 \\ x-coordiante=1.5 \end{gathered}[/tex]
c) y-coordinate
[tex]\begin{gathered} y-coordinate=r*sin\theta \\ replace \\ y-continent=-3*\sin(\frac{-2\pi}{3}) \\ y-continent=-3*-\frac{\sqrt{3}}{2} \\ y-continent=\frac{3\sqrt{3}}{2} \end{gathered}[/tex]
so, the answer is
[tex](\frac{3}{2},\frac{3\sqrt{3}}{2})[/tex]
I hope this helps you
